Problem: Simplify; express your answer in exponential form. Assume $x\neq 0, z\neq 0$. $\dfrac{{(x^{4})^{5}}}{{(x^{3}z^{-4})^{-1}}}$
Explanation: To start, try working on the numerator and the denominator independently. In the numerator, we have ${x^{4}}$ to the exponent ${5}$ . Now ${4 \times 5 = 20}$ , so ${(x^{4})^{5} = x^{20}}$ In the denominator, we can use the distributive property of exponents. ${(x^{3}z^{-4})^{-1} = (x^{3})^{-1}(z^{-4})^{-1}}$ Simplify using the same method from the numerator and put the entire equation together. $\dfrac{{(x^{4})^{5}}}{{(x^{3}z^{-4})^{-1}}} = \dfrac{{x^{20}}}{{x^{-3}z^{4}}}$ Break up the equation by variable and simplify. $\dfrac{{x^{20}}}{{x^{-3}z^{4}}} = \dfrac{{x^{20}}}{{x^{-3}}} \cdot \dfrac{{1}}{{z^{4}}} = x^{{20} - {(-3)}} \cdot z^{- {4}} = x^{23}z^{-4}$.